Appendix III.
925
out the extra bars, and find the forces in every member, calling
them Fsl, FS2, &c. Then, taking in the extra bars,
whole stress'! f force caused"! ["force caused
in I- = static force +••[ by stress in J--M by stress in
any member J [ extra bar a } ( extra bar b
••• F! - Fsl + ,-laFa + ^bFb.....................(3)
and so on for six equations, corresponding to the bars of the
structure. But
, /
Hence from (i) we have, eliminating-—^-
(from 3 and 4) = c^m^ (Fsl + rlaFa +• rlbFb)
4- ...........................
This is the final equation for bar a. From (2) we have :
(Fsl -h fiaFa 4- ^ibFb)
..................(7)
which is the final equation for bar b.
In like manner there would always be as many equations as
extra bars, and as many parts on the right side of each equation
as there might be ' static' bars.
Now," in using these equations practically, Fa and Fb are not
known, but c&......c^ and ^b......^6b are known from the shape of
the structure, Fsl......B^ from the static diagram, and ml to m^
m^ and m^ from the length, sectional area, and E of the respective
bars. Hence we have two simple simultaneous equations (6)
and (7), from which to find the values Fa and Fb- When these
are worked out, the stress in the other bars can be found from (3)
and (4).